5 papers
Supersolution Construction and Optimal Hardy Inequality for Fractional Laplacians
Philipp Hake, Matthias Keller, Felix Pogorzelski
We give a new criterion to show optimality of Hardy weights for general operators on graphs via the supersolution construction. For Laplacians on graphs without killing terms this…
A Liouville Theorem for Domains in Graphs
Philipp Hake, Matthias Keller, Felix Pogorzelski +1
We show a Liouville theorem for domains in graphs with Dirichlet boundary conditions. More specifically, we characterize the non-existence of non-zero bounded harmonic functions. S…
The complex property of the boundary operator on simplicial complexes
Philipp Bartmann, Matthias Keller
We study the complex property of the boundary operator on a weighted, infinite, and possibly non-locally finite simplicial complex. We give a char…
Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians
Philipp Hake, Matthias Keller, Felix Pogorzelski
We characterize positive critical Hardy weights for general Laplacians on weighted graphs. We then apply this result to fractional Laplacians on general graphs and use the characte…
Graphs at infinity: Liouville theorems, Recurrence and Characterization of Dirichlet forms
Matthias Keller, Daniel Lenz, Marcel Schmidt
We survey recent results on graphs and their Laplacians related to the behavior of the graph at large. In particular, we focus on Liouville theorems, recurrence and characterizatio…